Purifying electron spectra from noisy pulses with machine learning using synthetic Hamilton matrices.

Photo-electron spectra obtained with intense pulses generated by free-electron lasers through self-amplified spontaneous emission are intrinsically noisy and vary from shot to shot. We extract the purified spectrum, corresponding to a Fourier-limited pulse, with the help of a deep neural network. It is trained on a huge number of spectra, each of them calculated by an extremely efficient propagation of the Schr\"odinger equation with synthetic Hamilton matrices and random realizations of fluctuating pulses. Since this training input does not explicitly address the dimensionality of the electron dynamics, the trained network can purify spectra for realistic 3D dynamics. We demonstrate our approach with resonant two-photon ionization, a non-linear process which is particularly sensitive to pulse fluctuations.